Yes, Subject to DM Approval
There is a section in the PHB entitled "Variant: Skills with Different Abilities". The two specific examples they give are using Constitution on an Athletics check to swim an unusually far distance, and:
Similarly, when your half-orc barbarian uses a display of raw strength to intimidate an enemy, your DM might ask for a Strength (Intimidation) check, even though Intimidation is normally associated with Charisma. -PHB p. 175
Naturally, any Ability switching would be subject to DM approval. The rule is a "Variant", and thus might not be adopted by all DMs. Even if it is adopted by your DM, they are the decider for when it is applicable, and it might not be doable for all characters within a group. A DM might rule that you can't use another Ability unless you're proficient in the check, for example. In fact, the RAW only explicitly mentions checks you are proficient in:
In some situations, though, your proficiency might reasonably apply to a different kind of check. In such cases, the DM might ask for a check using an unusual combination of ability and skill, or you might ask your DM if you can apply a proficiency to a different check. -PHB p. 175
But there is RAW support for switching Abilities.